Chance and order: fractals, cellular automata and biology (year 2019)

In this section we present a research on "Chance and Order" with examples involving fractals in two and three dimensions, cellular automata and a biological model shaping a human heart. Each ordered structure will be shown following four different approches.
  1. Ordered structers plotted as "wholes" (static images)
  2. Ordered structures plotted according to an ordered sequential dynamics generating order starting from ordered initial conditions (animations)
  3. Ordered structures plotted according to a random dynamics generating order starting from random initial conditions (animations)
  4. Ordered structures plotted according by cellular automata generating order starting from random initial conditions (animations)

All the approaches reveal how information (law) coded into a computer program (algorithm) drives the evolutionary process towards an attractor (final image) both when order is manifestly evident just starting from the initial conditions and when order is hidden within a random assignement of the initial conditions themselves. In the latter situation order appears gradually as long as the process evolves as if it would arise from chance. In effect order is hidden by chance and it appears only step by step. The result appears especially interesting in applications to biology where the presence of a code governs the rise of life which only appearantly seems to emerge from chance. In fact it is experimentally known how totipotent stem cells can rebuild an enitre missing organ replicating themselves somehow randomly but following in the same time a coded information driving the generation process.

A detailed exposition is offered in A. Strumia, Information as order hidden within chance. From fractals and cellular automata to biology (World Scientific, 2020).